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I was never convinced by the "not being anywhere near Caemlyn" part. The Forsaken all have Traveling, any of them could have Traveled to some spot outside the city, masked their ability, waltzed on in and done the deed, and left again, in under a day.
Reading over the notes and Terez's comments, I get the impression that RJ may have changed his mind about Asmodean's killer but not updated all his notes to be consistent with the change; so perhaps he did actually have Graendal in mind when TFoH was published, even though there were some old contradictory notes in existence.
In the books, only a handful of the COTF are greenseers. It also says that normal COTF are long-lived (not clear quite how long), but greenseers only live perhaps 200 years - unless they decide to get weirwood-rootified
The ter'angreal actually use saidar and/or saidin to operate, even if the person activating it is not a channeler. They can draw the Power on their own.
JBear: "Looks like a massive khalasar has been here, swirling around a central point. Probably nothing." Daario: [walking over to centre] "Look , a ring!" JBear: "Khaleesi's ring" Daario+JBear: [eyes meet]
Speaking as a parent... they had been entrusted with Harry's upbringing, so sending him away to an untrusted location for 9 months would be irresponsible. Perhaps they would have loved nothing more than to get rid of him, but they felt responsible for ensuring his safety.